How to rephrase "Deliberate failure"?

Did anyone notice that your sentence describes merely the "grounds for punishment". So punishment is at your discretion. Its a warning, not a threat. You're saying what could happen, not what will happen. You're saying you won't assume it was deliberate. Retaining that element of humanity in your grammar shows that you recognize an element of humanity in them – the (essential) ability to choose, and also to make mistakes. Ask yourself, are you writing this to persuade them to do the right thing, or is this line simply to absolve you of possible legal repercussions?

I would keep it as simple as possible. "Remove X from all company computers. Failure to do so constitutes grounds for punishment."

Personally, I don't think 'compliance' is a nice word to use when talking about people's actions. And dictionary definitions give only the most basic etymology of words. When you're concerned with the tone and extended meanings associated with words, its good to know where they come from and in what context they're typically used. We don't talk about businesses 'behaving'. Why talk about people complying (unless you want them to focus on the legal implications of everything they do. Ugly!)

Further reading: http://www.amazon.com/Jurismania-Madness-American-Historical-Institute/dp/0195130839

Noncompliance constitutes grounds for punishment.

You are telling them so if they don't it would be deliberate. You are asking them to comply.

failure to follow an official rule or obey a law

I think "deliberate failure" clearly implies "knowingly and willfully" ignoring the instructions. It does not imply that simply forgetting once will get someone in trouble. Don't change anything.

It sounds like you expect people to:

engage in a good faith effort to remove X from all company computers whenever X is observed to be present

That would be sufficient in a contract. If your audience does not understand that this is a contract they are required to follow, then remind them of that.

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